Kamel Omar, a member of the opposition Popular Congress Party, was arrested without a warrant at his home, a spokesman was reported by the BBC to have said.
Khartoum accused him of having links to rebel groups in the restive Darfur region and for playing a role in anti-government protests.
Student protests erupted in Khartoum and elsewhere in the country last month after the government unveiled austerity measures. Sudan's economy has struggled since a January decision by South Sudan to halt oil production. South Sudan controls most of the regional oil fields while Sudan hosts export routes.
Protest groups have since called on the government of Sudanese President Omar al-Bashir to step aside.
Victoria Nuland, a spokeswoman for the U.S. State Department, said Tuesday Washington was "deeply concerned" with the treatment of dissidents in Sudan. Violence, she said, is no way to resolve national grievances.
"Sudan faces serious challenges that cannot be solved by suppressing dissenting views and forcibly disrupting peaceful demonstrations," she said in a statement.